it's not solid geometry, rather, it can be explained by group theory, one of the many branches of axiomatic mathematics. Group theory is partly concerned with "algebraic structures." - - - a 'set' with an 'operation' applied to it (for example: real numbers under the operation addition). In terms of the cube, it's algebraic structure can be identified as the 'set of all possible combinations' under the operation 'F', 'L', 'R,' 'U,' 'B,' 'D' - - - Furthermore, it can also explain why there are "impossible configurations" in scrambling (applying random operations) the cube.

_________________LET:>>cxcxc be a Rubik's Cube>>U be the set of all tangible Rubik's Cubes,>>i.e., U={cxcxc | c is an integer and lies in the interval [2,11]}>>C be the set of my cubes on hand>>S={2, 3, 4, 5}MY CUBES ON HAND CAN BE THE DESCRIBED BY THE SET C where...>>C={nxnxn element of set U | n is an element of S}